The century-old Gauss-Markov theorem (GMT)
showed that the ordinary least squares (OLS) estimator (sample mean)
is the (minimum variance) best (efficient) linear unbiased estimator (BLUE).
[1]} shocked statisticians when he
proved the inadmissibility of OLS, and
threw
the first
salvo toward the break-up of the
long-dominating GMT.
Numerous subsequent papers established that the
so-called Stein-rule (nonlinear shrinkage) estimator is
guaranteed to reduce the mean squared error (MSE) of OLS.
[2]} explain
the practical significance of Stein-rule in
a Scientific American magazine article (May 1977)
using baseball batting averages. The key point of the
Stein-rule is that despite the GMT BLUE result,
shrinkage estimation beats OLS.
